On the Generating Function of Specialized Mechanisms with Design Constraints

• Main Authors: Lin, Shu-Hong, 林書弘
• Other Authors: Hwang, Yii-Wen
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/52982388875398007381

博士 === 國立中正大學 === 機械工程學系暨研究所 === 100 === This research proposes an innovative methodology to generate specialized mechanism, without having to check for an isomorphic mechanism. The first step in this methodology is the derivation of a permutation from a labeled kinematic chain, according to the combinatorial theory. Then, the permutation is analyzed to obtain a composite permutation group. The composite permutation group contains basic permutation groups and operators. In this thesis, six basic permutation groups and four operators explained and defined by the permutations. Every basic permutation group has its own generating function and computation, using the operators derives the generating function of the kinematic chain. The generating function is a polynomial, which allots a name to links, or joints of the kinematic chain, in specialization. Type synthesis defines a design constraint to sieve the solution from the kinematic chain. Three design constrains are discussed in this thesis; adjacent, incident and path constraints. The generating function of the kinematic chain is sieved by the design constrains and a specialized generating function is obtained, which shows the result of the specialization process. The innovative mathematical method proposed here uses the generating function and coefficient to efficiently and accurately identify specialized mechanisms, thereby solving the problem of specialization in type synthesis. Being systematic, the method avoids the disadvantages of the observation method in the specialization process, and, as the numerical results show, eliminates the need to inspect for isomorphism in order to identify the exact mechanisms.